Related papers: Probability-Density-Based Deep Learning Paradigm f…

Traditional domain generalization methods often rely on domain alignment to reduce inter-domain distribution differences and learn domain-invariant representations. However, domain shifts are inherently difficult to eliminate, which limits…

Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we…

Probabilistic circuits (PCs) represent a probability distribution as a computational graph. Enforcing structural properties on these graphs guarantees that several inference scenarios become tractable. Among these properties, structured…

Despite exceptional predictive performance of Deep sequence models (DSMs), the main concern of their deployment centers around the lack of uncertainty awareness. In contrast, probabilistic models quantify the uncertainty associated with…

A key challenge facing deep learning is that neural networks are often not robust to shifts in the underlying data distribution. We study this problem from the perspective of the statistical concept of parameter identification.…

Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…

Fusing probabilistic information is a fundamental task in signal and data processing with relevance to many fields of technology and science. In this work, we investigate the fusion of multiple probability density functions (pdfs) of a…

Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent…

The simulation of nanophotonic structures relies on electromagnetic solvers, which play a crucial role in understanding their behavior. However, these solvers often come with a significant computational cost, making their application in…

Mechanical and phononic metamaterials exhibiting negative elastic moduli, gapped vibrational spectra, or topologically protected modes enable precise control of structural and acoustic functionalities. While much progress has been made in…

Why rely on dense neural networks and then blindly sparsify them when prior knowledge about the problem structure is already available? Many inverse problems admit algorithm-unrolled networks that naturally encode physics and sparsity. In…

Diffusion models indirectly estimate the probability density over a data space, which can be used to study its structure. In this work, we show that geodesics can be computed in diffusion latent space, where the norm induced by the…

A machine learning model that generalizes well should obtain low errors on unseen test examples. Thus, if we learn an optimal model in training data, it could have better generalization performance in testing tasks. However, learning such a…

Mixture models whose components have skewed hypercube contours are developed via a generalization of the multivariate shifted asymmetric Laplace density. Specifically, we develop mixtures of multiple scaled shifted asymmetric Laplace…

This paper introduces a new notion of dimensionality of probabilistic models from an information-theoretic view point. We call it the "descriptive dimension"(Ddim). We show that Ddim coincides with the number of independent parameters for…

In this paper, we focus on approximating a natural class of functions that are compositions of smooth functions. Unlike the low-dimensional support assumption on the covariate, we demonstrate that composition functions have an intrinsic…

We introduce the concept of maximum probability domains (MPDs), developed in the context of the analysis of electronic densities, in the study of the microscopic spatial structures of liquids. The idea of locating a particle in a three…

Random features is a powerful universal function approximator that inherits the theoretical rigor of kernel methods and can scale up to modern learning tasks. This paper views uncertain system models as unknown or uncertain smooth functions…

Load balancing is the process of improving the Performance of a parallel and distributed system through is distribution of load among the processors [1-2]. Most of the previous work in load balancing and distributed decision making in…

While deep learning offers powerful capabilities for scientific research, its application is often hindered by a lack of quantitative reliability. To address this, we introduce a probabilistic denoising framework that simultaneously…